Two slabs $A$ and $B$ of equal surface area are placed one over the other such that their surfaces are…
Two slabs $A$ and $B$ of equal surface area are placed one over the other such that their surfaces are completely in contact. The thickness of slab $A$ is twice that of $B$. The coefficient of thermal conductivity of slab $A$ is twice that of $B$. The first surface of slab $A$ is maintained at $100^{\circ} \mathrm{C}$, while the second surface of slab $B$ is maintained at $25^{\circ} \mathrm{C}$. The temperature at the contact of their surfaces is
$62.5^{\circ} \mathrm{C}$
$45^{\circ} \mathrm{C}$
$55^{\circ} \mathrm{C}$
$85^{\circ} \mathrm{C}$
Solution
The temperature at the contact of the surface
$
\begin{aligned}
& =\frac{K_1 d_2 \theta_1+K_2 d_1 \theta_2}{K_1 d_2+K_2 d_1} \\
& =\frac{2 K_2 d_2 \times 100+2 d_2 \times K_2 \times 25}{2 K_2 d_2+K_2 2 d_2} \\
& =\frac{200+50}{4}=62.5^{\circ} \mathrm{C}
\end{aligned}
$